Integral and Derivative Rules Flashcards

1
Q

Derivative of the absolute value of u

A

(u/abs. value u)(u’)

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2
Q

Derivative sinx

A

cosx

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3
Q

Derivative cosx

A

-sinx

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4
Q

Derivative tanx

A

sec^2x

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5
Q

Derivative cscx

A

-cscxcotx

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6
Q

Derivative secx

A

secxtanx

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7
Q

Derivative cotx

A

-csc^2x

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8
Q

Derivative lnx

A

x’/x

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9
Q

Derivative log(little x)u

A

(u’/u) (1/lnx)

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10
Q

Derivative e^x

A

e^x (x’)

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11
Q

Derivative a^x

A

a^x (x’) (lna)

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12
Q

derivative ln absolute value x

A

x’/x

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13
Q

Derivative of inverse of f(x)

A

1/f’(f^-1(x))

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14
Q

Derivative arcsinu

A

u’/(1-u^2)^.5

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15
Q

Derivative arctanu

A

u’ / (1+u^2)

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16
Q

Derivative arcsecu

A

u’ / IuI(u^2-1)^.5

17
Q

Integral 1/x

A

Ln IxI + C

18
Q

Integral e^x

A

e^x + C

19
Q

Integral a^x

A

(a^x / lna) + C

20
Q

Integral sinx

A

-cosx+c

21
Q

Integral cosx

A

sinx + C

22
Q

Integral tanx

A

-Ln IcosxI + C

23
Q

Integral cotx

A

Ln IsinxI +C

24
Q

Integral cscx

A

-Ln Icscx + cotxI + C

25
Q

Integral secx

A

Ln Isecx + tanxI + C

26
Q

Integral sec^2x

A

tanx + C

27
Q

Integral csc^2x

A

-cotx + C

28
Q

Integral secxtanx

A

secx + C

29
Q

Integral cscxcotx

A

-cscx + C

30
Q

Integral du/root a^2-u^2

A

arcsin u/a + C

31
Q

Integral du/ u root u^2-a^2

A

1/a arcsec IuI/a + C

32
Q

Integral du/ a^2+u^2

A

1/a arctan u/a + C